The Federal Reserve on Thursday gave clean bills of health to most of the largest American banks, allowing them to return money to shareholders, but it forced Goldman Sachs and Morgan Stanley to freeze such payouts around last year’s levels.

The Fed said that all of the nation’s very biggest banks — Bank of America, Wells Fargo, Citigroup, Goldman Sachs, Morgan Stanley and JPMorgan Chase — passed the second round of the central bank’s “stress tests,” which gauge whether financial institutions have enough capital and are sufficiently well-managed to continue lending during periods of financial upheaval.

The tests were intended to gauge the health of 35 banks, and regulators said they would allow 34 of them to pay dividends and buy back their own shares, a boon for investors who have been eager to benefit from the banks’ record profits.

The banks will almost certainly use their collective success to amplify their argument that, 10 years after the financial crisis, they do not need to be as tightly regulated, and that they deserve relief similar to what their much smaller peers received earlier this year when President Trump signed a bill easing parts of the Dodd-Frank law, the landmark bank oversight legislation enacted in 2010.

The six largest American banks got permission to pay out a combined sum of more than $125 billions in the form of increased dividends, which reward investors for every share of stock they own, and share buybacks, which increase the value of a company’s stock by reducing the number of shares outstanding.

The only bank to fail the stress test was the American arm of Germany’s Deutsche Bank, which Fed officials sharply criticized for “widespread and critical deficiencies” in how it handles its capital and manages its finances. The Fed’s grievances mean Deutsche Bank will be restricted from transferring money from the United States to its Frankfurt headquarters, potentially making its Wall Street operations less lucrative at a time when the bank’s top executives are already mulling cuts to that business.

In an emailed statement, the American arm of Deutsche Bank said that it “continues to make progress across a range of programs and will continue to build on these efforts and to engage constructively with regulators to meet both internal and regulatory expectations.”

The Fed also dealt an embarrassing blow to Goldman and Morgan Stanley, which each fell below minimum capital levels. The banks were given “conditional approval” to return money to shareholders, but they were required to keep their shareholder payouts near last year’s levels and work on beefing up their capital cushions over the next year.

But that is likely to be only a temporary hiccup for the two Wall Street titans. Goldman and Morgan Stanley fell short largely because the tax law that Mr. Trump signed late last year caused them to record large, one-time accounting losses. Going forward, the cuts will most likely generate enormous tax savings for both firms, which would make it easier for them to win approval to reward shareholders.

Lloyd Blankfein, Goldman’s chief executive, said in a statement that the bank is “positioned to return capital to our shareholders, while reinvesting in our global client franchise for the long-term.”

Goldman is allowed to pay out $6.3 billion this year compared to $5.7 billion last year, while Morgan Stanley’s permitted payout was the same as last year’s actual distribution: $6.8 billion.

Image

Wells Fargo has faced several regulatory and legal challenges but on Thursday, the Federal Reserve said it was strong enough to return capital to its shareholders.CreditDevin Yalkin for The New York Times

Several other financial institutions scaled back their planned payouts in order to win the Fed’s blessing, including JPMorgan Chase, KeyCorp, M&T Bank and American Express.

Wells Fargo, which has suffered a string of regulatory and legal problems for deceiving customers, passed the test and received approval to return about $32.9 billion to shareholders, more than double the value of last year’s permitted payout. But part of the reason the bank had so much cash available for shareholders is a result of governmental intervention: Earlier this year, the Fed ordered Wells Fargo to stop growing until it improved its internal operations enough to prevent further rule violations.

State Street, a so-called custody bank whose biggest customers are institutions, not individuals, also received only conditional approval for its plans to reward shareholders. Fed officials said State Street had not been properly assessing the risk of its exposure to other financial players, although the central bank ultimately gave a green light to State Street to distribute cash to its shareholders.

The Fed’s criticism is notable because State Street, among others, lobbied successfully this spring for lawmakers to reduce certain capital requirements that custody banks face. When calculating how much capital to hold on their balance sheets, State Street and two other custody banks are able to set aside deposits they received from other banks and immediately gave to the Federal Reserve or another central bank.

State Street did not comment specifically on the Fed’s criticism. But in a statement published on its website, the bank said that it was not being required to resubmit its cash distribution plan after making the regulator’s requested changes.

Fed Vice Chairman Randal K. Quarles said in a statement on Thursday that the test results “demonstrate that the largest banks have strong capital levels, and after making their approved capital distributions, would retain their ability to lend even in a severe recession.”

The 35 banks that went through the stress tests have added $800 billion in high-quality capital since 2009, the Fed said. While those banks would lose $578 billion during a severe recession, the Fed concluded that they would be able to keep lending in such an environment.

Last week, the Fed said all 35 banks had passed the first of two hurdles in their yearly evaluations, which test how financial institutions would hold up if the economy sank into a recession. The Fed’s stress tests, put in place in the wake of the 2008 financial crisis, consider a variety of economic scenarios, including a spike in unemployment and cratering house prices. Thursday’s round of tests also included a “qualitative” assessment that evaluated whether banks have adequate internal controls and risk management systems to ensure they can detect potential problems before they escalate.

Both tests form the basis of the regulator’s decision about whether to let the banks distribute some of their cash to shareholders through buybacks and dividends. For foreign banks, the tests determine how much capital they can send back their parent companies overseas.

These days, there’s plenty of cash to hand out.

In the first three months of 2018, bank profits increased 27.5 percent from the same period last year, the Federal Deposit Insurance Corporation reported in May. The Fed’s interest-rate increases and Mr. Trump’s tax cuts fueled the bumper profits. JPMorgan Chase, Wells Fargo and Bank of America already have reported saving a total of about $8 billion thanks to the tax cuts, according to the research group Just Capital.

Citigroup, JPMorgan Chase and Bank of America may now distribute $22 billion, $31.6 billion and $26 billion, respectively, according to company statements and calculations by The New York Times.

The Fed’s announcement on Thursday that most banks can plow ahead with big dividend payouts and share buybacks is likely to provide ammunition to Democrats who already have been attacking the tax cuts as a giveaway to big banks and wealthy shareholders. After last year’s tests, banks announced their largest dividend payouts in nearly a decade.

Peter Eavis contributed reporting.

A version of this article appears in print on , on Page B1 of the New York edition with the headline: Fed Clears the Way for Banks To Reward Their Shareholders. Order Reprints | Today’s Paper | Subscribe